A three-dimensional model of the varistor device is proposed. The thermal and electric conductivity of the material are taken to depend, in addition to the electric potential, on the temperature. Two theorems of existence and uniqueness of solutions for the boundary-value problem which determine the potential and the temperature inside the device are proposed. Levy–Caccioppoli global inversion theorem is used for the proof.

Using lock-in infrared microscopy as a tool for current detection on the micrometer scale in AC-driven specimens in combination with iterative grinding procedure allows preparation of current dominating microstructure regions on well-polished surfaces. This technique is applied successfully on varistor components based on specially doped ZnO-based varistor ceramics. This peculiar electroceramic material exhibits exceptional high nonlinear current–voltage (I-V) characteristics, described by a power law according I~Vα, caused by double Schottky barriers at the grain boundaries. As a novelty the thermographic response is used to evaluate local electrical properties, namely the nonlinearity coefficient α, on basis of higher order harmonics with respect to the basic electrical driving AC-frequency.

To correlate the observed electrical properties to the microstructure, the polar crystal orientation of the relevant ZnO grains is determined by combining electron backscatter diffraction and orientation-dependent patterns as a result of a chemical etching procedure. These findings support a modified new model for describing the grain boundary controlled current flow in a varistor microstructure including orientation-dependent barrier properties. Hence, the experimentally observed current direction-dependent behavior can be described consistently.